A long-running dispute between the U.S. and China over the ability to vet auditors of Chinese companies listed on American exchanges is edging toward a possible breakthrough.

Two big U.S.-listed Chinese companies—Alibaba Group Holding Ltd. and Baidu Inc.—and their outside auditors are preparing for audit inspections by officials from the Public Company Accounting Oversight Board, the U.S. audit-industry regulator. The PCAOB is expected to gain access in coming months to audit firms’ records of the work they did to review Alibaba’s...